[tex]z^{7}=128i[/tex]

z = ____ + ____ i

Answers

Answer 1

If z ⁷ = 128i, then there are 7 complex numbers z that satisfy this equation.

[tex]z^7 = 128i = 2^7i = 2^7e^{i\frac\pi2}[/tex]

[tex]\implies z=\sqrt[7]{2^7} e^{i\frac17\left(\frac\pi2+2n\pi\right)}[/tex]

(where n = 0, 1, 2, …, 6)

[tex]\implies z = 2 e^{i\left(\frac\pi{14}+\frac{2n\pi}7\right)}[/tex]

[tex]\displaystyle\implies z = 2 \left(\cos\left(\frac\pi{14}+\frac{2n\pi}7\right)+i\sin\left(\frac\pi{14}+\frac{2n\pi}7\right)\right)[/tex]


Related Questions

If the relationship is proportional, what is the missing value from the table
x
-12
-1
?
-10
-30
O-8
-6
-5
04

Answers

Given:

Consider the below figure attached with this question.

The table represents a proportional relationship.

To find:

The missing value from the table.

Solution:

If y is proportional to x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]                 ...(i)

Where, k is a constant of proportionality.

The relationship passes through the point (-3,-1). Substituting [tex]x=-3,y=-1[/tex] in (i), we get

[tex]-1=k(-3)[/tex]

[tex]\dfrac{-1}{-3}=k[/tex]

[tex]\dfrac{1}{3}=k[/tex]

Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get

[tex]y=\dfrac{1}{3}x[/tex]           ...(ii)

We need to find the y-value for [tex]x=-12[/tex].

Substituting [tex]x=-12[/tex] in (ii), we get

[tex]y=\dfrac{1}{3}(-12)[/tex]

[tex]y=-4[/tex]

Therefore, the missing value in the table is -4. Hence, option D is correct.

2.6.67
Two cylindrical cans of soup sell for the same price. One can has a diameter of 6 inches and a height of 7 inches. The other has a diameter of 7 inches and a height
of 6 inches. Which can contains more soup and, therefore, is the better buy?
Which can contains more soup and therefore, is the better buy?

Please help :)

Answers

Answer:

second can

Step-by-step explanation:

The radius is half of the diameter.

The radius is squared in the formula for the volume of the cylinder.

A diameter of 7 and height of 6 will make a larger can than a diameter of 6 and height of 7.

How to find B?
what type of angle is it?

Answers

90 minus 43 = 47 . Answer is 47

Answer:

Obtuse angle; 57°

Step-by-step explanation:

b and 43° form a right angle. A right angle is 90°. Solution: 90°-43°=57°

43° is acute, so angle b must be obtuse.

How to find the surface area of a this cuboid

Answers

Answer:

40

Step-by-step explanation:

There are 6 sides. Four sides have 8 squares, 4 * 2, and the other 2 sides have 4, 2 * 2. 8 * 4 = 32, 4 * 2 = 8, 32 + 8 = 40

A school band found they could arrange themselves in rows of 6, 7, or 8 with no one left over. What is the minimum number of students in the band?

Answers

Answer:

168 is the answer if i m not wrong.I took the LCM.

If school band found they could arrange themselves in rows of 6, 7, or 8 with no one left over, the minimum number of students in the band is 168.

To find the minimum number of students in the band, we need to determine the least common multiple (LCM) of the numbers 6, 7, and 8.

The LCM is the smallest multiple that is divisible by all the given numbers.

Prime factorizing each number, we have:

6 = 2 * 3

7 = 7

8 = 2 * 2 * 2

To find the LCM, we take the highest exponent for each prime factor:

2³ * 3 * 7 = 168

By having 168 students, they can arrange themselves into rows of 6 (28 rows), 7 (24 rows), or 8 (21 rows) without anyone being left over. Any fewer than 168 students would result in at least one row having students left over.

To learn more about LCM click on,

https://brainly.com/question/1771764

#SPJ2

2. Find the Perimeter AND Area of the
figure below.
5 in.
6 in.
8 in.
9 in.

Answers

Area: 64 in.
Perimeter: 102 in.

Can someone please help me

Answers

Answer:

sorry I can't help you sorry

Answer:

c

Step-by-step explanation:

A reflection in the x- axis of the parent function is - [tex]\sqrt{x}[/tex]

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here the shift is 3 units up , then

g(x) = - [tex]\sqrt{x}[/tex] + 3

State the final conclusion in simple nontechnical terms.
Original claim: The proportion of male golfers is less than 0.6.
Initial conclusion: Fail to reject the null hypothesis.
Which of the following is the correct conclusion?
A. There is suffficient evidence to support the claim that the proportion of male golfers is less than 0.6.
B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.

Answers

Answer:

B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.

Step-by-step explanation:

The proportion of male golfers is less than 0.6.

At the null hypothesis, we test if the proportion is of at least 0.6, that is:

[tex]H_0: p \geq 0.6[/tex]

At the alternative hypothesis, we test if the proportion is of less than 0.6, that is:

[tex]H_1: p < 0.6[/tex]

Fail to reject the null hypothesis.

This means that there is not sufficient evidence to conclude that the proportion is less than 0.6, and thus the correct answer is given by option B.

The graph shows the solution of the following system of equations. y = –5∕3x + 3 y = 1∕3x – 3

Answers

Answer:

So whats your question ??

Step-by-step explanation:

Question 1
Assume that a procedure yields a binomial distribution.
n = 48 p = 0.44. Find the mean.

Answers

Answer:

The mean is 21.12.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this question:

[tex]n = 48, p = 0.44[/tex]

Mean:

[tex]E(X) = np = 48(0.44) = 21.12[/tex]

The mean is 21.12.

What is the solution to this system of equations?

Answers

Answer:

(2,1)

Step-by-step explanation:

the graph intersects at 2 and 1

-5(4-n)=1+2n
Anyone know this

Answers

Answer:

n= -10

Step-by-step explanation:

-20+n=1+2n which simplifies to -21n+n=2n which simplifies to -20n=2n which simplifies to

n= -10

what tearm means per hundred
a.base b.percent c.percentage d.rate​

Answers

the term per hundred means percent

hope it helps

Answer:

C. Percent

Explanation:

per hundred means 1 in 100. percent is referring to the unit that is 1 in 100 of another value

1ex. 1% of 100 (1 percent of 100)

2ex. 49% of 235 (49 percent of 235)

Evaluate -6-2x when x=-4

Answers

Answer:

2

Step-by-step explanation:

Given [tex]-6-2x[/tex] where [tex]x=-4[/tex], substitute [tex]x=-4[/tex] to find the value of the given equation.

Substituting [tex]x=-4[/tex]:

[tex]-6-2(-4)[/tex]

Multiply [tex]-2\cdot -4[/tex]:

[tex]-6+8[/tex]

Combine like terms:

[tex]-6+8=\boxed{2}[/tex]

Therefore, the value of [tex]-6-2x[/tex] when [tex]x=-4[/tex] is [tex]\boxed{2}[/tex].

help pls, stuck on this

Answers

Answer:

Step-by-step explanation:

Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) c, c, c , where c > 0

Answers

Answer:

cos(∝) = 1/√3

cos(β) = 1/√3

cos(γ) = 1/√3

∝ = 55°

β = 55°

γ = 55°

Step-by-step explanation:

Given the data in the question;

vector is z = < c,c,c >

the direction cosines and direction angles of the vector = ?

Cosines are the angle made with the respect to the axes.

cos(∝) = z < 1,0,0 > / |z|

so

cos(∝) = < c,c,c > < 1,0,0 > / √[c² + c² + c²] = ( c + 0 + 0 ) / √[ 3c² ]

cos(∝) = c / √[ 3c² ] = c / c√3 = 1/√3

∝ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

cos(β) = < c,c,c > < 0,1,0 > / √[c² + c² + c²] = ( 0 + c + 0 ) / √[ 3c² ]

cos(β) = c / √[ 3c² ] = c / c√3 = 1/√3

β = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

cos(γ) = < c,c,c > < 0,0,1 > / √[c² + c² + c²] = ( 0 + 0 + c ) / √[ 3c² ]

cos(γ) = c / √[ 3c² ] = c / c√3 = 1/√3

γ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

Therefore;

cos(∝) = 1/√3

cos(β) = 1/√3

cos(γ) = 1/√3

∝ = 55°

β = 55°

γ = 55°

A party supply company makes cone shaped party hats for children using thin cardboard. To the nearest square centimeter, how much cardboard is required to make the party hate use pie = 3.14.

Answers

Answer:

A. 754 cm²

Step-by-step explanation:

Amount of cardboard needed = surface area of the cone

Curved surface area of the cone = πrl

Where,

π = 3.14

r = ½(20) = 10 cm

l = 24 cm

Plug in the values into the formula

Curved surface area = 3.14 × 10 × 24 = 753.6 ≈ 754 cm²

if an orange weighs 570 grams what is the weight of an apple​

Answers

Answer:

THE SAME

Step-by-step explanation:

how many crores are there in 20 million​

Answers

Answer:

20 million = 2 crore

Step-by-step explanation:

Here we will show you how to convert 20 million to crores (twenty million in crores). This may be useful if you for example want to convert 20 million rupees to crore rupees or 20 million dollars to crore dollars.

In some parts of the world like the United States, large numbers are separated with commas in three-digit-interval format like this:

...,BBB,MMM,TTT,HHH

BBB = billions

MMM = millions

TTT = thousands

HHH = hundreds

In certain parts of Asia, the format is a little different. From right to left, it starts out with three digits followed by a comma like the US, but after that, it is in intervals of two digits like this:

..,AA,CC,LL,TT,HHH

AA = arabs

CC = crores

LL = lakhs

TT = thousands

HHH = hundreds

Below we have displayed 20 million with the two number systems, based on the information above:

MM,TTT,HHH

20,000,000

=

C,LL,TT,HHH

2,00,00,000

When you match up 20 million with the C,LL,TT,HHH format above, you can see what 20 million is in crores. The answer to 20 million in crores is as follows:

20 million

= 2 crore

Question 2
A force F=5i+3j-2k is applied to move a block of cement from A(0,1,1) to B(4.-1,3).
Determine the work done by the force.

Answers

The work is simply the dot product of the force and displacement (which I assume are given in Newtons and meters, respectively):

W = F • d

W = (5i + 3j - 2k) N • ((4i - j + 3k) m - (j + k) m)

W = (5i + 3j - 2k) • (4i - 2j + 2k) Nm

W = (20 - 6 - 4) Nm

W = 10 J

If someone can pls give the answer with steps that would be greatly appreciated :)

Answers

Answer:

1.Sentence examples for that would be greatly appreciated from inspiring English sources. If Norton or Symantec or anyone else can provide any info that would be greatly appreciated!! In all sincerity, if Hillary supporters at The Daily Beast and Daily Banter can enlighten us, that would be greatly appreciated.

Hope It helps

Membership A equation is c=5v+30
Membership B equation is c=10v

Now plug in the number 1-10 into the v variable and solve the equation

SCALCET8 3.9.003. Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm2

Answers

Answer: [tex]24\ cm^2/s[/tex]

Step-by-step explanation:

Given

Each side of square is increasing at a rate of 4 cm/s

Side of a square when area is [tex]9\ cm^2[/tex]

Suppose a is side of the square

[tex]\Rightarrow a=\sqrt{9}\\\Rightarrow a=3\ cm[/tex]

Area is given by

[tex]\Rightarrow A=a^2\\\text{Differentiate area w.r.t time}\\\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 3\times 4\\\\\Rightarrow \dfrac{dA}{dt}=24\ cm^2/s[/tex]

Area is increasing at a rate of [tex]24\ cm^2/s[/tex]

Answer:

24cm^2/ s

Step-by-step explanation:

Annual entertainment expenses in a population of 100 families have a mean of $2040 and a standard deviation of $360.
(a) Find the mean and standard deviation of monthly expenses.
(b) What is the total amount of monthly entertainment expenses for this population?

Answers

Answer:

The correct answer is:

(a) Mean = 170,

    Standard deviation = 30

(b) 1700

Step-by-step explanation:

Given:

n = 100μ = 2040σ = 360

(a)

Mean of monthly expenses will be:

= [tex]\frac{\mu}{2}[/tex]

= [tex]\frac{2040}{2}[/tex]

= [tex]170[/tex]

Standard deviation will be:

= [tex]\frac{\sigma}{12}[/tex]

= [tex]\frac{360}{12}[/tex]

= [tex]30[/tex]

(b)

The total amount of monthly expenses will be:

= [tex]n\times \frac{\mu}{12}[/tex]

= [tex]100\times 170[/tex]

= [tex]1700[/tex]

Step by step solution help me pls

Answers

Step-by-step explanation:

Recall that

[tex]1 + \tan^2 x = \sec^2 x[/tex]

and

[tex]\dfrac{d}{dx}(\tan x) = \sec^2 x[/tex]

so that

[tex]\displaystyle \int \tan^2 x = \int (\sec^2 x - 1)dx[/tex]

[tex]\:\:\:\:\:\:\:\:\:=\int \sec^2 xdx - \int dx[/tex]

[tex]\:\:\:\:\:\:\:\:\:=\tan x - x + C[/tex]

where C is the constant of integration.

Jan is as old as Gary was 15 years ago. Six years from now, Gary will be twice as old as Jan will be then. How old is Gary now?

Answers

Answer:

Gary is now 24years

Step-by-step explanation:

let the age of Jan be x and that of Gary be x+15

in six years time they will be as follows

Jan =x+6

Gary=x+15+6=x+21

2(x+6)=x+21

2x+12=x+21

collect the like terms

2x-x=21-12

x=9

Gary =9+15=24years

Số táo của An Bình Chi là như nhau. An cho đi 17 quả, Chi cho đi 19 quả thì lúc đó số táo của Chi gấp 5 lần tổng số táo của An và Bình. Hỏi lúc đầu mỗi bạn có bao nhiêu quả táo?( Giải bài toán trên bằng phương trình hoặc hệ phương trình )

Answers

Answer:

please write in english i cannot understand

Step-by-step explanation:

Which of the following statements are true?

Answers

Answer:

D

Step-by-step explanation:

i think it's correct if not I'm sorry

I have sons but no daughter ,each of my sons has twice as many brothers as he has children . each of my sons has same no of children each of my grand children has many cousins as uncle. how many grand children do I have ?

Answers

Answer:

Step-by-step explanation:

keeping track of family relations can be difficult. If Edna marries your mother’s uncle Charlie, what should you call her? If your father’s cousin’s daughter just had a baby boy, how should you two be introduced? Who is your “great great aunt”, and how can you find your “first cousin twice removed”? Fortunately, a bit of mathematical logic can clarify who should be called what, and why – and even measure the degree of genetic similarity between different relatives.

Joanne's monthly salary is $2400.she spend's ⅒ of it on food and ⅜ of it on leisure activities.How much does she have left?​

Answers

Answer:

1200$

please mark me as brain liest

The vertical test line

Answers

Step-by-step explanation:

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines. and, as a result, any vertical line in the plane can intersect the graph of a function at most once.

hope it helpsstay safe healthy and happy....

Answer:

It is a graphical method

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